A variety of catheter tube holders are provided by prior art patents. One example is a catheter tube holder which has two adhesive members connected by an adhesive narrow bridge to secure the members in a doubled over form when the two main members are used to position a catheter tube to a patient. Another example is catheter tube anchoring device system which has an adhesively-attachable single-piece having two channels connected by a bridge, each channel for receiving a tubular segment. However, what is needed is an adhesively-attachable H-shaped catheter tube anchoring device having two flexible side members and a rigid crossmember therebetween, the crossmember having a retainer mounted thereto for receiving a catheter tube and for holding the catheter tube at a 3-degree angle and further having two rigid vertically-oriented gripping tabs, one on each side of the retainer, to be gripped while advancing the catheter forward in piercing the vein with a needle, thus reducing the risk of contaminating the catheter, thereby reducing the risk of patient infection, while also making starting an I.V. easier and faster. The present catheter tube anchoring device addresses the foregoing needs by providing an adhesively-attachable H-shaped catheter tube anchoring device which two flexible side members and a rigid crossmember therebetween, the crossmember having a retainer mounted thereto for receiving a catheter tube and for holding the catheter tube at a 3-degree angle and further having two gripping tabs, one on each side of the retainer, assisting in the advancement of a catheter needle into a patient's vein and in the attachment of a catheter adaptor to I.V. tubing.